Causal Inference Assignment

#Question 1

# Importing the data
library(readr)
d=read_csv("https://bit.ly/2SKjUn2")

Rows: 16 Columns: 5── Column specification ─────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (1): treat
dbl (4): id, block, reg_voters, vote_pop
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

#Get treatment vector as a dummy
treatment=numeric(length(d$treat))
treatment[d$treat=="pub.pol"]=1


mean(d$vote_pop[treatment == 1]) - mean(d$vote_pop[treatment == 0])

[1] -0.1575

View(d)

#Create 12870 permutations of assignment
vec <- c(rep(0,8),rep(1,8))
tbl_v <- table(vec)
library(RcppAlgos)

Warning: package ‘RcppAlgos’ was built under R version 4.3.2

treat_permutations <- permuteGeneral(names(tbl_v), 16, freqs = tbl_v)
as.numeric(treat_permutations[1,])

 [1] 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1

dim(treat_permutations)

[1] 12870    16

# Fisher Exact Test (a)

library(progress)

Warning: package ‘progress’ was built under R version 4.3.2

# Function to calculate treatment effect
calculate_treatment_effect <- function(df) {
  mean(df$vote_pop[df$treat == 1]) - mean(df$vote_pop[df$treat == 0])
}

# Initialize a dataframe
results_df <- data.frame(permutation = integer(12870), treatment_effect = numeric(12870))

pb <- progress_bar$new(total = dim(treat_permutations)[1], clear = FALSE, format = "  :current/:total [:bar] :percent")

# Iterate over each permutation and calculate treatment effect
for (i in 1:nrow(treat_permutations)) {
  
  pb$tick()
  
  d$treat <- as.numeric(treat_permutations[i,])
  treatment_effect <- calculate_treatment_effect(d)

  # Store permutation and corresponding treatment effect
  results_df[i, ] <- list(permutation = paste(as.numeric(treat_permutations[i, ]), collapse = ""), treatment_effect = treatment_effect)
}

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# Print the first few rows of the results dataframe
head(results_df)

#Plotting null randomization distribution

library(ggplot2)

ggplot(results_df, aes(x = treatment_effect)) +
  geom_histogram(binwidth = 0.020, fill = "blue", color = "black", alpha = 0.7) +
  labs(title = "Histogram of 12,870 Test Statistics", x = "Difference of Means", y = "Frequency") +
  theme_minimal() +
  theme(plot.title = element_text(hjust = 0.5)) +
  geom_vline(xintercept = -0.1575,color='red') +
  annotate("text", x = -0.215, y = 750, label = "Observed Test Statistic",size=2.65) 

# Getting p-value of observed test statistic

extreme_count <- sum(results_df$treatment_effect <= -0.1575)
p_value = extreme_count/length(results_df$treatment_effect)
p_value

[1] 0.04662005

# Calculating treatment effects by block to get observed test statistic

library(readr)
d=read_csv("https://bit.ly/2SKjUn2")

Rows: 16 Columns: 5── Column specification ─────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (1): treat
dbl (4): id, block, reg_voters, vote_pop
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

treatment=numeric(length(d$treat))
treatment[d$treat=="pub.pol"]=1
by_block <- d %>% group_by(block)
treatment_effects <- (by_block %>% summarise(treatment = diff(vote_pop)))$treatment
treatment_effects

[1] -0.21 -0.05 -0.01 -0.56 -0.01 -0.14 -0.10 -0.18

mean(treatment_effects)

[1] -0.1575

# Extra credit

library(gtools)

Warning: package ‘gtools’ was built under R version 4.3.2

library(progress)
library(readr)
d=read_csv("https://bit.ly/2SKjUn2")

Rows: 16 Columns: 5── Column specification ─────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (1): treat
dbl (4): id, block, reg_voters, vote_pop
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

treatment=numeric(length(d$treat))
treatment[d$treat=="pub.pol"]=1

# Function to replace 'A' with (0,1) and 'B' with (1,0)
replace_pairs <- function(permutation) {
  sapply(permutation, function(x) {
    if (x == 'A') {
      return(c(0, 1))
    } else {
      return(c(1, 0))
    }
  })
}

# Generate all permutations
perm_strings <- permutations(n = 2, r = 8, v = c('A', 'B'), repeats.allowed = TRUE)

# Apply the replacement function to each permutation, transpose to have rows
# as the treatment/control permutation
block_permutations <- t(apply(perm_strings, 1, replace_pairs))



library(progress)
calculate_treatment_effect <- function(df) {
  mean(df$vote_pop[df$treat == 1]) - mean(df$vote_pop[df$treat == 0])}
block_results_df <- data.frame(permutation = integer(256), treatment_effect = numeric(256))

pb <- progress_bar$new(total = dim(block_permutations)[1], clear = FALSE, format = "  :current/:total [:bar] :percent")

# Iterate over each permutation and calculate treatment effect
for (i in 1:nrow(block_permutations)) {
  pb$tick()
  
  # Update the 'treat' column in the dataframe
  d$treat <- block_permutations[i,]

  # Calculate the treatment effect for this permutation
  treatment_effect <- calculate_treatment_effect(d)

  # Store the permutation and its treatment effect
  block_results_df[i, ] <- list(permutation = paste(block_permutations[i,], collapse = ""), treatment_effect = treatment_effect)
}

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head(block_results_df)

library(ggplot2)

ggplot(block_results_df, aes(x = treatment_effect)) +
  geom_histogram(bins = 27, fill = "blue", color = "black", alpha = 0.7) +
  labs(title = "Histogram of 256 Test Statistics", x = "Difference of Means", y = "Frequency") +
  theme_minimal() +
  theme(plot.title = element_text(hjust = 0.5)) +
  geom_vline(xintercept = -0.1575,color='red') +
  annotate("text", x = -0.12, y = 30, label = "Observed Test Statistic",size=2.65) 

min(block_results_df$treatment_effect)

[1] -0.1575

block_p_value = 1/256

length(unique(block_results_df$treatment_effect))

[1] 135

Modes <- function(x) {
  ux <- unique(x)
  tab <- tabulate(match(x, ux))
  ux[tab == max(tab)]
}
Modes(block_results_df$treatment_effect)

[1] -0.075  0.065 -0.065  0.075

# Question 2

library(readr)
library(Matching)
library(dplyr)

gb <- read_csv("C:/Users/raphael khalid/Desktop/CS130 Causal Inference/greenbuildings.csv")

Rows: 7820 Columns: 16── Column specification ─────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr  (1): class
dbl (15): CS_PropertyID, rev_psf, Rent, leasing_rate, size, City_Market_Rent, stories, age, renovated, gr...
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

# Method 1: Encoding class to numeric
gb <- gb %>%
  mutate(class = case_when(
    class == "A" ~ 1,
    class == "B" ~ 2,
    class == "C" ~ 3))
gb

attach(gb)
Tr <- green_rating
X <- cbind(size, stories, age, class)
Y <- leasing_rate
detach(gb)

# Perform genetic matching
gen1 <- GenMatch(Tr = Tr, X = X, wait.generations=5, max.generations = 20)

Sun Nov 26 14:35:58 2023
Domains:
 0.000000e+00   <=  X1   <=    1.000000e+03 
 0.000000e+00   <=  X2   <=    1.000000e+03 
 0.000000e+00   <=  X3   <=    1.000000e+03 
 0.000000e+00   <=  X4   <=    1.000000e+03 

Data Type: Floating Point
Operators (code number, name, population) 
    (1) Cloning...........................  15
    (2) Uniform Mutation..................  12
    (3) Boundary Mutation.................  12
    (4) Non-Uniform Mutation..............  12
    (5) Polytope Crossover................  12
    (6) Simple Crossover..................  12
    (7) Whole Non-Uniform Mutation........  12
    (8) Heuristic Crossover...............  12
    (9) Local-Minimum Crossover...........  0

SOFT Maximum Number of Generations: 20
Maximum Nonchanging Generations: 5
Population size       : 100
Convergence Tolerance: 1.000000e-03

Not Using the BFGS Derivative Based Optimizer on the Best Individual Each Generation.
Not Checking Gradients before Stopping.
Using Out of Bounds Individuals.

Maximization Problem.
GENERATION: 0 (initializing the population)
Lexical Fit..... 8.042622e-02  1.919202e-01  2.660542e-01  3.173109e-01  3.464481e-01  5.588048e-01  6.792199e-01  1.000000e+00  
#unique......... 100, #Total UniqueCount: 100
var 1:
best............ 4.052061e+02
mean............ 4.606271e+02
variance........ 8.881056e+04
var 2:
best............ 3.533284e+02
mean............ 4.935909e+02
variance........ 8.184157e+04
var 3:
best............ 9.126206e+02
mean............ 5.273906e+02
variance........ 7.603680e+04
var 4:
best............ 2.245625e+02
mean............ 4.757956e+02
variance........ 9.977177e+04

GENERATION: 1
Lexical Fit..... 1.608458e-01  1.930106e-01  3.157635e-01  3.173109e-01  3.667090e-01  5.202268e-01  6.705182e-01  1.000000e+00  
#unique......... 71, #Total UniqueCount: 171
var 1:
best............ 3.352935e+02
mean............ 5.698992e+02
variance........ 5.264302e+04
var 2:
best............ 3.533284e+02
mean............ 3.954249e+02
variance........ 2.571046e+04
var 3:
best............ 9.126206e+02
mean............ 7.291094e+02
variance........ 3.145122e+04
var 4:
best............ 2.245625e+02
mean............ 4.590147e+02
variance........ 7.595013e+04

GENERATION: 2
Lexical Fit..... 1.608458e-01  1.930106e-01  3.157635e-01  3.173109e-01  3.667090e-01  5.202268e-01  6.705182e-01  1.000000e+00  
#unique......... 65, #Total UniqueCount: 236
var 1:
best............ 3.352935e+02
mean............ 4.088098e+02
variance........ 2.243200e+04
var 2:
best............ 3.533284e+02
mean............ 3.682769e+02
variance........ 6.589972e+03
var 3:
best............ 9.126206e+02
mean............ 8.494079e+02
variance........ 2.679277e+04
var 4:
best............ 2.245625e+02
mean............ 2.773730e+02
variance........ 3.101895e+04

GENERATION: 3
Lexical Fit..... 1.608458e-01  1.930106e-01  3.157635e-01  3.173109e-01  3.667090e-01  5.202268e-01  6.705182e-01  1.000000e+00  
#unique......... 53, #Total UniqueCount: 289
var 1:
best............ 3.352935e+02
mean............ 3.532617e+02
variance........ 5.891582e+03
var 2:
best............ 3.533284e+02
mean............ 3.672782e+02
variance........ 7.015408e+03
var 3:
best............ 9.126206e+02
mean............ 8.876973e+02
variance........ 6.864194e+03
var 4:
best............ 2.245625e+02
mean............ 2.389426e+02
variance........ 6.598408e+03

GENERATION: 4
Lexical Fit..... 1.608458e-01  1.930106e-01  3.157635e-01  3.173109e-01  3.667090e-01  5.202268e-01  6.705182e-01  1.000000e+00  
#unique......... 48, #Total UniqueCount: 337
var 1:
best............ 3.352935e+02
mean............ 3.620538e+02
variance........ 1.104401e+04
var 2:
best............ 3.533284e+02
mean............ 3.463538e+02
variance........ 2.828694e+03
var 3:
best............ 9.126206e+02
mean............ 8.955470e+02
variance........ 3.623274e+03
var 4:
best............ 2.245625e+02
mean............ 2.373075e+02
variance........ 1.697853e+03

GENERATION: 5
Lexical Fit..... 1.633750e-01  1.712549e-01  2.865335e-01  3.173109e-01  3.217826e-01  4.704898e-01  5.270278e-01  1.000000e+00  
#unique......... 43, #Total UniqueCount: 380
var 1:
best............ 3.327124e+02
mean............ 3.359501e+02
variance........ 9.148943e+03
var 2:
best............ 3.354284e+02
mean............ 3.631542e+02
variance........ 3.269580e+03
var 3:
best............ 9.209369e+02
mean............ 9.059576e+02
variance........ 3.170516e+03
var 4:
best............ 2.704413e+02
mean............ 2.390905e+02
variance........ 1.161777e+04

GENERATION: 6
Lexical Fit..... 1.652548e-01  1.776384e-01  3.082385e-01  3.173109e-01  3.199033e-01  4.962837e-01  5.249102e-01  1.000000e+00  
#unique......... 68, #Total UniqueCount: 448
var 1:
best............ 3.330652e+02
mean............ 3.473089e+02
variance........ 6.517667e+03
var 2:
best............ 3.378746e+02
mean............ 3.498031e+02
variance........ 5.068334e+03
var 3:
best............ 9.198004e+02
mean............ 8.975045e+02
variance........ 1.046789e+04
var 4:
best............ 2.641715e+02
mean............ 2.651337e+02
variance........ 9.397933e+03

GENERATION: 7
Lexical Fit..... 1.712549e-01  1.725861e-01  2.972509e-01  3.173109e-01  3.199033e-01  4.683888e-01  5.249102e-01  1.000000e+00  
#unique......... 63, #Total UniqueCount: 511
var 1:
best............ 3.328894e+02
mean............ 3.403083e+02
variance........ 3.553280e+03
var 2:
best............ 3.366555e+02
mean............ 3.416056e+02
variance........ 3.700417e+03
var 3:
best............ 9.202717e+02
mean............ 9.071357e+02
variance........ 2.666225e+03
var 4:
best............ 2.672961e+02
mean............ 2.600746e+02
variance........ 6.479322e+03

GENERATION: 8
Lexical Fit..... 1.712549e-01  1.725861e-01  2.972509e-01  3.173109e-01  3.199033e-01  4.683888e-01  5.249102e-01  1.000000e+00  
#unique......... 69, #Total UniqueCount: 580
var 1:
best............ 3.328894e+02
mean............ 3.435979e+02
variance........ 2.214998e+03
var 2:
best............ 3.366555e+02
mean............ 3.368251e+02
variance........ 1.782525e+03
var 3:
best............ 9.202717e+02
mean............ 9.044187e+02
variance........ 9.000972e+03
var 4:
best............ 2.672961e+02
mean............ 2.844040e+02
variance........ 7.224846e+03

GENERATION: 9
Lexical Fit..... 1.712549e-01  1.725861e-01  2.972509e-01  3.173109e-01  3.199033e-01  4.683888e-01  5.249102e-01  1.000000e+00  
#unique......... 66, #Total UniqueCount: 646
var 1:
best............ 3.328894e+02
mean............ 3.355783e+02
variance........ 9.195697e+03
var 2:
best............ 3.366555e+02
mean............ 3.416592e+02
variance........ 4.252466e+03
var 3:
best............ 9.202717e+02
mean............ 9.060154e+02
variance........ 7.361790e+03
var 4:
best............ 2.672961e+02
mean............ 2.742951e+02
variance........ 4.223172e+03

GENERATION: 10
Lexical Fit..... 1.712549e-01  1.725861e-01  2.972509e-01  3.173109e-01  3.199033e-01  4.683888e-01  5.249102e-01  1.000000e+00  
#unique......... 63, #Total UniqueCount: 709
var 1:
best............ 3.328894e+02
mean............ 3.369063e+02
variance........ 3.675374e+03
var 2:
best............ 3.366555e+02
mean............ 3.476796e+02
variance........ 3.889934e+03
var 3:
best............ 9.202717e+02
mean............ 9.022044e+02
variance........ 1.166949e+04
var 4:
best............ 2.672961e+02
mean............ 2.701802e+02
variance........ 7.555463e+02

GENERATION: 11
Lexical Fit..... 1.712549e-01  1.725861e-01  2.972509e-01  3.173109e-01  3.199033e-01  4.683888e-01  5.249102e-01  1.000000e+00  
#unique......... 64, #Total UniqueCount: 773
var 1:
best............ 3.328894e+02
mean............ 3.283296e+02
variance........ 1.560590e+03
var 2:
best............ 3.366555e+02
mean............ 3.456409e+02
variance........ 3.603916e+03
var 3:
best............ 9.202717e+02
mean............ 8.998141e+02
variance........ 8.126906e+03
var 4:
best............ 2.672961e+02
mean............ 2.821737e+02
variance........ 8.242839e+03

GENERATION: 12
Lexical Fit..... 1.712549e-01  1.725861e-01  2.972509e-01  3.173109e-01  3.199033e-01  4.683888e-01  5.249102e-01  1.000000e+00  
#unique......... 69, #Total UniqueCount: 842
var 1:
best............ 3.328894e+02
mean............ 3.414497e+02
variance........ 3.055453e+03
var 2:
best............ 3.366555e+02
mean............ 3.464776e+02
variance........ 4.539931e+03
var 3:
best............ 9.202717e+02
mean............ 9.091441e+02
variance........ 4.291132e+03
var 4:
best............ 2.672961e+02
mean............ 2.699546e+02
variance........ 1.272190e+03

GENERATION: 13
Lexical Fit..... 1.712549e-01  1.725861e-01  2.972509e-01  3.173109e-01  3.199033e-01  4.683888e-01  5.249102e-01  1.000000e+00  
#unique......... 67, #Total UniqueCount: 909
var 1:
best............ 3.328894e+02
mean............ 3.335695e+02
variance........ 1.716758e+03
var 2:
best............ 3.366555e+02
mean............ 3.338593e+02
variance........ 8.498696e+02
var 3:
best............ 9.202717e+02
mean............ 9.043458e+02
variance........ 6.103111e+03
var 4:
best............ 2.672961e+02
mean............ 2.816272e+02
variance........ 1.057014e+04

'wait.generations' limit reached.
No significant improvement in 5 generations.

Solution Lexical Fitness Value:
1.712549e-01  1.725861e-01  2.972509e-01  3.173109e-01  3.199033e-01  4.683888e-01  5.249102e-01  1.000000e+00  

Parameters at the Solution:

 X[ 1] :    3.328894e+02
 X[ 2] :    3.366555e+02
 X[ 3] :    9.202717e+02
 X[ 4] :    2.672961e+02

Solution Found Generation 7
Number of Generations Run 13

Sun Nov 26 14:38:29 2023
Total run time : 0 hours 2 minutes and 31 seconds

mgen1 <- Match(Tr=Tr, X=X, Weight.matrix=gen1)
MatchBalance(Tr~size + stories + age + class, data=gb, match.out=mgen1, nboots=1000)  

***** (V1) size *****
                       Before Matching       After Matching
mean treatment........     326101            326101 
mean control..........     226158            324538 
std mean diff.........     34.366           0.53729 

mean raw eQQ diff.....     106293             11449 
med  raw eQQ diff.....     111749            5994.5 
max  raw eQQ diff.....    2059803            148788 

mean eCDF diff........    0.16972         0.0084028 
med  eCDF diff........    0.20193         0.0058594 
max  eCDF diff........    0.27229          0.034505 

var ratio (Tr/Co).....    0.95638            1.0036 
T-test p-value........ < 2.22e-16           0.17259 
KS Bootstrap p-value.. < 2.22e-16             0.318 
KS Naive p-value...... < 2.22e-16            0.3199 
KS Statistic..........    0.27229          0.034505 


***** (V2) stories *****
                       Before Matching       After Matching
mean treatment........     15.343            15.343 
mean control..........     13.424            15.278 
std mean diff.........     14.413           0.48655 

mean raw eQQ diff.....      1.947           0.52604 
med  raw eQQ diff.....          2                 0 
max  raw eQQ diff.....         34                14 

mean eCDF diff........   0.027321         0.0073317 
med  eCDF diff........    0.01588         0.0052083 
max  eCDF diff........    0.08163          0.029297 

var ratio (Tr/Co).....      1.191            1.0618 
T-test p-value........ 0.00032045           0.29725 
KS Bootstrap p-value.. < 2.22e-16             0.399 
KS Naive p-value...... 0.00051562           0.52491 
KS Statistic..........    0.08163          0.029297 


***** (V3) age *****
                       Before Matching       After Matching
mean treatment........     23.898            23.898 
mean control..........     49.308                24 
std mean diff.........    -162.69          -0.65065 

mean raw eQQ diff.....     25.454           0.59635 
med  raw eQQ diff.....         14                 0 
max  raw eQQ diff.....         63                 8 

mean eCDF diff........    0.17859         0.0066438 
med  eCDF diff........    0.15303         0.0045573 
max  eCDF diff........    0.44503          0.030599 

var ratio (Tr/Co).....    0.23341           0.99419 
T-test p-value........ < 2.22e-16           0.17125 
KS Bootstrap p-value.. < 2.22e-16             0.298 
KS Naive p-value...... < 2.22e-16           0.46839 
KS Statistic..........    0.44503          0.030599 


***** (V4) class *****
                       Before Matching       After Matching
mean treatment........      1.215             1.215 
mean control..........     1.7929            1.2135 
std mean diff.........    -132.68           0.33815 

mean raw eQQ diff.....    0.57879         0.0019531 
med  raw eQQ diff.....          1                 0 
max  raw eQQ diff.....          1                 1 

mean eCDF diff........    0.19262        0.00065104 
med  eCDF diff........    0.14373                 0 
max  eCDF diff........    0.43413         0.0019531 

var ratio (Tr/Co).....    0.40157            1.0204 
T-test p-value........ < 2.22e-16           0.31731 
KS Bootstrap p-value.. < 2.22e-16             0.972 
KS Naive p-value...... < 2.22e-16                 1 
KS Statistic..........    0.43413         0.0019531 


Before Matching Minimum p.value: < 2.22e-16 
Variable Name(s): size stories age class  Number(s): 1 2 3 4 

After Matching Minimum p.value: 0.17125 
Variable Name(s): age  Number(s): 3 

mgenout_main <- Match(Y=Y, Tr=Tr, X=X, Weight.matrix=gen1)
summary(mgenout_main)

Estimate...  2.7948 
AI SE......  0.88627 
T-stat.....  3.1535 
p.val......  0.0016133 

Original number of observations..............  7820 
Original number of treated obs...............  679 
Matched number of observations...............  679 
Matched number of observations  (unweighted).  1536 

# Method 2: Using class_a and class_b
Tr <- gb$green_rating
X <- cbind(gb$size, gb$stories, gb$age, gb$class_a, gb$class_b)
Y <- gb$leasing_rate
# Perform genetic matching
gen2 <- GenMatch(Tr = Tr, X = X, wait.generations=5, max.generations = 20)

Sun Nov 26 14:39:12 2023
Domains:
 0.000000e+00   <=  X1   <=    1.000000e+03 
 0.000000e+00   <=  X2   <=    1.000000e+03 
 0.000000e+00   <=  X3   <=    1.000000e+03 
 0.000000e+00   <=  X4   <=    1.000000e+03 
 0.000000e+00   <=  X5   <=    1.000000e+03 

Data Type: Floating Point
Operators (code number, name, population) 
    (1) Cloning...........................  15
    (2) Uniform Mutation..................  12
    (3) Boundary Mutation.................  12
    (4) Non-Uniform Mutation..............  12
    (5) Polytope Crossover................  12
    (6) Simple Crossover..................  12
    (7) Whole Non-Uniform Mutation........  12
    (8) Heuristic Crossover...............  12
    (9) Local-Minimum Crossover...........  0

SOFT Maximum Number of Generations: 20
Maximum Nonchanging Generations: 5
Population size       : 100
Convergence Tolerance: 1.000000e-03

Not Using the BFGS Derivative Based Optimizer on the Best Individual Each Generation.
Not Checking Gradients before Stopping.
Using Out of Bounds Individuals.

Maximization Problem.
GENERATION: 0 (initializing the population)
Lexical Fit..... 6.617208e-02  1.563606e-01  2.011898e-01  3.214068e-01  5.558594e-01  6.764728e-01  1.000000e+00  1.000000e+00  1.000000e+00  1.000000e+00  
#unique......... 100, #Total UniqueCount: 100
var 1:
best............ 4.167930e+02
mean............ 4.933432e+02
variance........ 8.318411e+04
var 2:
best............ 3.676719e+02
mean............ 5.180173e+02
variance........ 9.272120e+04
var 3:
best............ 8.611146e+02
mean............ 4.744151e+02
variance........ 7.132562e+04
var 4:
best............ 6.808970e+02
mean............ 4.769405e+02
variance........ 6.448677e+04
var 5:
best............ 3.906511e+02
mean............ 5.052198e+02
variance........ 7.623197e+04

GENERATION: 1
Lexical Fit..... 1.251692e-01  1.828491e-01  2.318151e-01  3.157635e-01  5.494971e-01  6.705182e-01  1.000000e+00  1.000000e+00  1.000000e+00  1.000000e+00  
#unique......... 70, #Total UniqueCount: 170
var 1:
best............ 4.205235e+02
mean............ 5.253988e+02
variance........ 3.700991e+04
var 2:
best............ 3.776825e+02
mean............ 4.583559e+02
variance........ 4.918821e+04
var 3:
best............ 8.539813e+02
mean............ 6.867676e+02
variance........ 3.798343e+04
var 4:
best............ 6.784862e+02
mean............ 5.683985e+02
variance........ 3.839920e+04
var 5:
best............ 3.904160e+02
mean............ 4.389003e+02
variance........ 3.162648e+04

GENERATION: 2
Lexical Fit..... 1.286983e-01  1.979268e-01  2.318151e-01  3.153868e-01  5.490705e-01  6.701179e-01  1.000000e+00  1.000000e+00  1.000000e+00  1.000000e+00  
#unique......... 72, #Total UniqueCount: 242
var 1:
best............ 4.223455e+02
mean............ 4.604950e+02
variance........ 1.255964e+04
var 2:
best............ 3.825718e+02
mean............ 4.356688e+02
variance........ 2.991022e+04
var 3:
best............ 8.548856e+02
mean............ 7.763030e+02
variance........ 2.118401e+04
var 4:
best............ 6.478468e+02
mean............ 6.877564e+02
variance........ 2.391806e+04
var 5:
best............ 2.968313e+02
mean............ 4.197790e+02
variance........ 1.077737e+04

GENERATION: 3
Lexical Fit..... 2.130178e-01  2.228403e-01  2.257325e-01  3.173109e-01  3.173109e-01  3.387277e-01  5.503494e-01  6.713175e-01  1.000000e+00  1.000000e+00  
#unique......... 67, #Total UniqueCount: 309
var 1:
best............ 4.205235e+02
mean............ 4.281401e+02
variance........ 2.966934e+03
var 2:
best............ 3.776825e+02
mean............ 3.756880e+02
variance........ 1.463988e+03
var 3:
best............ 8.539813e+02
mean............ 8.288127e+02
variance........ 6.103752e+03
var 4:
best............ 6.784862e+02
mean............ 6.512296e+02
variance........ 1.137064e+04
var 5:
best............ 4.061264e+01
mean............ 3.426891e+02
variance........ 1.273395e+04

GENERATION: 4
Lexical Fit..... 2.257325e-01  2.289469e-01  2.313313e-01  3.173109e-01  3.173109e-01  3.387277e-01  5.503494e-01  6.713175e-01  1.000000e+00  1.000000e+00  
#unique......... 64, #Total UniqueCount: 373
var 1:
best............ 4.205235e+02
mean............ 4.405893e+02
variance........ 5.927552e+03
var 2:
best............ 3.820828e+02
mean............ 3.790845e+02
variance........ 8.131019e+02
var 3:
best............ 8.547952e+02
mean............ 8.507574e+02
variance........ 1.335416e+03
var 4:
best............ 6.509108e+02
mean............ 6.372770e+02
variance........ 1.305401e+04
var 5:
best............ 1.017628e+02
mean............ 1.771690e+02
variance........ 1.750305e+04

GENERATION: 5
Lexical Fit..... 2.257325e-01  2.289469e-01  2.313313e-01  3.173109e-01  3.173109e-01  3.387277e-01  5.503494e-01  6.713175e-01  1.000000e+00  1.000000e+00  
#unique......... 72, #Total UniqueCount: 445
var 1:
best............ 4.205235e+02
mean............ 4.279408e+02
variance........ 6.154285e+03
var 2:
best............ 3.820828e+02
mean............ 3.939903e+02
variance........ 4.323083e+03
var 3:
best............ 8.547952e+02
mean............ 8.290622e+02
variance........ 8.434302e+03
var 4:
best............ 6.509108e+02
mean............ 6.519526e+02
variance........ 1.628751e+03
var 5:
best............ 1.017628e+02
mean............ 1.126918e+02
variance........ 4.108949e+03

GENERATION: 6
Lexical Fit..... 2.257325e-01  2.289469e-01  2.313313e-01  3.173109e-01  3.173109e-01  3.387277e-01  5.503494e-01  6.713175e-01  1.000000e+00  1.000000e+00  
#unique......... 70, #Total UniqueCount: 515
var 1:
best............ 4.205235e+02
mean............ 4.279851e+02
variance........ 1.812899e+03
var 2:
best............ 3.820828e+02
mean............ 3.791438e+02
variance........ 6.609076e+02
var 3:
best............ 8.547952e+02
mean............ 8.368578e+02
variance........ 5.325107e+03
var 4:
best............ 6.509108e+02
mean............ 6.509051e+02
variance........ 2.752408e+03
var 5:
best............ 1.017628e+02
mean............ 1.278893e+02
variance........ 1.095819e+04

GENERATION: 7
Lexical Fit..... 2.257325e-01  2.289469e-01  2.313313e-01  3.173109e-01  3.173109e-01  3.387277e-01  5.503494e-01  6.713175e-01  1.000000e+00  1.000000e+00  
#unique......... 70, #Total UniqueCount: 585
var 1:
best............ 4.205235e+02
mean............ 4.216556e+02
variance........ 3.734218e+03
var 2:
best............ 3.820828e+02
mean............ 3.888572e+02
variance........ 3.728513e+03
var 3:
best............ 8.547952e+02
mean............ 8.351424e+02
variance........ 8.190935e+03
var 4:
best............ 6.509108e+02
mean............ 6.455101e+02
variance........ 4.516313e+03
var 5:
best............ 1.017628e+02
mean............ 1.185964e+02
variance........ 8.644706e+03

GENERATION: 8
Lexical Fit..... 2.257325e-01  2.289469e-01  2.313313e-01  3.173109e-01  3.173109e-01  3.387277e-01  5.503494e-01  6.713175e-01  1.000000e+00  1.000000e+00  
#unique......... 62, #Total UniqueCount: 647
var 1:
best............ 4.205235e+02
mean............ 4.288746e+02
variance........ 1.923616e+03
var 2:
best............ 3.820828e+02
mean............ 3.834202e+02
variance........ 1.033148e+03
var 3:
best............ 8.547952e+02
mean............ 8.420717e+02
variance........ 8.731370e+03
var 4:
best............ 6.509108e+02
mean............ 6.411260e+02
variance........ 3.079931e+03
var 5:
best............ 1.017628e+02
mean............ 1.187620e+02
variance........ 8.025674e+03

GENERATION: 9
Lexical Fit..... 2.257325e-01  2.289469e-01  2.313313e-01  3.173109e-01  3.173109e-01  3.387277e-01  5.503494e-01  6.713175e-01  1.000000e+00  1.000000e+00  
#unique......... 66, #Total UniqueCount: 713
var 1:
best............ 4.205235e+02
mean............ 4.196103e+02
variance........ 4.063391e+02
var 2:
best............ 3.820828e+02
mean............ 3.914577e+02
variance........ 5.332421e+03
var 3:
best............ 8.547952e+02
mean............ 8.543921e+02
variance........ 4.312481e+02
var 4:
best............ 6.509108e+02
mean............ 6.457589e+02
variance........ 5.866755e+03
var 5:
best............ 1.017628e+02
mean............ 1.028492e+02
variance........ 7.500681e+01

GENERATION: 10
Lexical Fit..... 2.257325e-01  2.289469e-01  2.313313e-01  3.173109e-01  3.173109e-01  3.387277e-01  5.503494e-01  6.713175e-01  1.000000e+00  1.000000e+00  
#unique......... 63, #Total UniqueCount: 776
var 1:
best............ 4.205235e+02
mean............ 4.285830e+02
variance........ 1.786946e+03
var 2:
best............ 3.820828e+02
mean............ 3.939976e+02
variance........ 7.734801e+03
var 3:
best............ 8.547952e+02
mean............ 8.474500e+02
variance........ 3.494192e+03
var 4:
best............ 6.509108e+02
mean............ 6.384906e+02
variance........ 6.944949e+03
var 5:
best............ 1.017628e+02
mean............ 1.085219e+02
variance........ 2.643119e+03

'wait.generations' limit reached.
No significant improvement in 5 generations.

Solution Lexical Fitness Value:
2.257325e-01  2.289469e-01  2.313313e-01  3.173109e-01  3.173109e-01  3.387277e-01  5.503494e-01  6.713175e-01  1.000000e+00  1.000000e+00  

Parameters at the Solution:

 X[ 1] :    4.205235e+02
 X[ 2] :    3.820828e+02
 X[ 3] :    8.547952e+02
 X[ 4] :    6.509108e+02
 X[ 5] :    1.017628e+02

Solution Found Generation 4
Number of Generations Run 10

Sun Nov 26 14:41:45 2023
Total run time : 0 hours 2 minutes and 33 seconds

mgen2 <- Match(Tr=Tr, X=X, Weight.matrix=gen2)
MatchBalance(Tr~size + stories + age + class_a + class_b, data=gb, match.out=mgen2, nboots=1000)

***** (V1) size *****
                       Before Matching       After Matching
mean treatment........     326101            326101 
mean control..........     226158            324859 
std mean diff.........     34.366           0.42699 

mean raw eQQ diff.....     106293             10320 
med  raw eQQ diff.....     111749              5376 
max  raw eQQ diff.....    2059803            148788 

mean eCDF diff........    0.16972         0.0077568 
med  eCDF diff........    0.20193         0.0058939 
max  eCDF diff........    0.27229          0.034054 

var ratio (Tr/Co).....    0.95638            1.0045 
T-test p-value........ < 2.22e-16           0.22895 
KS Bootstrap p-value.. < 2.22e-16             0.302 
KS Naive p-value...... < 2.22e-16           0.33873 
KS Statistic..........    0.27229          0.034054 


***** (V2) stories *****
                       Before Matching       After Matching
mean treatment........     15.343            15.343 
mean control..........     13.424            15.267 
std mean diff.........     14.413           0.57502 

mean raw eQQ diff.....      1.947           0.52914 
med  raw eQQ diff.....          2                 0 
max  raw eQQ diff.....         34                14 

mean eCDF diff........   0.027321         0.0073749 
med  eCDF diff........    0.01588         0.0058939 
max  eCDF diff........    0.08163          0.026195 

var ratio (Tr/Co).....      1.191             1.066 
T-test p-value........ 0.00032045           0.23133 
KS Bootstrap p-value.. < 2.22e-16             0.516 
KS Naive p-value...... 0.00051562           0.67132 
KS Statistic..........    0.08163          0.026195 


***** (V3) age *****
                       Before Matching       After Matching
mean treatment........     23.898            23.898 
mean control..........     49.308            23.993 
std mean diff.........    -162.69           -0.6035 

mean raw eQQ diff.....     25.454           0.61297 
med  raw eQQ diff.....         14                 0 
max  raw eQQ diff.....         63                 8 

mean eCDF diff........    0.17859         0.0067593 
med  eCDF diff........    0.15303          0.005239 
max  eCDF diff........    0.44503          0.028815 

var ratio (Tr/Co).....    0.23341           0.99681 
T-test p-value........ < 2.22e-16           0.22573 
KS Bootstrap p-value.. < 2.22e-16             0.382 
KS Naive p-value...... < 2.22e-16           0.55035 
KS Statistic..........    0.44503          0.028815 


***** (V4) class_a *****
                       Before Matching       After Matching
mean treatment........    0.79529           0.79529 
mean control..........    0.36115           0.79529 
std mean diff.........     107.51                 0 

mean raw eQQ diff.....    0.43446                 0 
med  raw eQQ diff.....          0                 0 
max  raw eQQ diff.....          1                 0 

mean eCDF diff........    0.21707                 0 
med  eCDF diff........    0.21707                 0 
max  eCDF diff........    0.43413                 0 

var ratio (Tr/Co).....    0.70658                 1 
T-test p-value........ < 2.22e-16                 1 


***** (V5) class_b *****
                       Before Matching       After Matching
mean treatment........     0.1944            0.1944 
mean control..........    0.48481           0.19588 
std mean diff.........    -73.328          -0.37188 

mean raw eQQ diff.....    0.29013         0.0019646 
med  raw eQQ diff.....          0                 0 
max  raw eQQ diff.....          1                 1 

mean eCDF diff........     0.1452        0.00098232 
med  eCDF diff........     0.1452        0.00098232 
max  eCDF diff........     0.2904         0.0019646 

var ratio (Tr/Co).....    0.62786            0.9943 
T-test p-value........ < 2.22e-16           0.31731 


Before Matching Minimum p.value: < 2.22e-16 
Variable Name(s): size stories age class_a class_b  Number(s): 1 2 3 4 5 

After Matching Minimum p.value: 0.22573 
Variable Name(s): age  Number(s): 3 

# Visual Inspection of Data Distribution

library(ggplot2)
# Create a histogram of treatment effects
ggplot(gb, aes(x = size)) +
  geom_histogram(bins = 30, fill = "blue", color = "black", alpha = 0.7) +
  labs(title = "Histogram of Size", x = "Size", y = "Frequency") +
  theme_minimal() +
  theme(plot.title = element_text(hjust = 0.5))

ggplot(gb, aes(x = stories)) +
  geom_histogram(bins = 30, fill = "blue", color = "black", alpha = 0.7) +
  labs(title = "Histogram of Stories", x = "Stories", y = "Frequency") +
  theme_minimal() +
  theme(plot.title = element_text(hjust = 0.5))

ggplot(gb, aes(x = age)) +
  geom_histogram(bins = 30, fill = "blue", color = "black", alpha = 0.7) +
  labs(title = "Histogram of Age", x = "Age", y = "Frequency") +
  theme_minimal() +
  theme(plot.title = element_text(hjust = 0.5))

ggplot(gb, aes(x = class)) +
  geom_histogram(bins = 30, fill = "blue", color = "black", alpha = 0.7) +
  labs(title = "Histogram of Class", x = "Class", y = "Frequency") +
  theme_minimal() +
  theme(plot.title = element_text(hjust = 0.5))

sd(gb$size)

[1] 298127.2

# Genetic matching with Caliper

attach(gb)
Tr <- green_rating
X <- cbind(size, stories, age, class)
Y <- leasing_rate
detach(gb)
caliper <- c(300/sd(gb$size),
             3/sd(gb$stories),
             3/sd(gb$age),
             1/sd(gb$class))
# Perform genetic matching
gen3 <- GenMatch(Tr = Tr, X = X, wait.generations=5, max.generations = 20, caliper= caliper)

Sun Nov 26 14:42:13 2023
Domains:
 0.000000e+00   <=  X1   <=    1.000000e+03 
 0.000000e+00   <=  X2   <=    1.000000e+03 
 0.000000e+00   <=  X3   <=    1.000000e+03 
 0.000000e+00   <=  X4   <=    1.000000e+03 

Data Type: Floating Point
Operators (code number, name, population) 
    (1) Cloning...........................  15
    (2) Uniform Mutation..................  12
    (3) Boundary Mutation.................  12
    (4) Non-Uniform Mutation..............  12
    (5) Polytope Crossover................  12
    (6) Simple Crossover..................  12
    (7) Whole Non-Uniform Mutation........  12
    (8) Heuristic Crossover...............  12
    (9) Local-Minimum Crossover...........  0

SOFT Maximum Number of Generations: 20
Maximum Nonchanging Generations: 5
Population size       : 100
Convergence Tolerance: 1.000000e-03

Not Using the BFGS Derivative Based Optimizer on the Best Individual Each Generation.
Not Checking Gradients before Stopping.
Using Out of Bounds Individuals.

Maximization Problem.
GENERATION: 0 (initializing the population)
Lexical Fit..... 1.085711e-02  5.588192e-02  2.121869e-01  2.122577e-01  8.836725e-01  9.153209e-01  1.000000e+00  1.000000e+00  
#unique......... 100, #Total UniqueCount: 100
var 1:
best............ 1.000000e+00
mean............ 5.163680e+02
variance........ 8.325095e+04
var 2:
best............ 1.000000e+00
mean............ 5.614413e+02
variance........ 8.880453e+04
var 3:
best............ 1.000000e+00
mean............ 5.636047e+02
variance........ 6.714905e+04
var 4:
best............ 1.000000e+00
mean............ 4.938942e+02
variance........ 9.671595e+04

GENERATION: 1
Lexical Fit..... 1.085711e-02  5.588192e-02  2.121869e-01  2.122577e-01  8.836725e-01  9.153209e-01  1.000000e+00  1.000000e+00  
#unique......... 68, #Total UniqueCount: 168
var 1:
best............ 1.000000e+00
mean............ 1.108718e+02
variance........ 4.365764e+04
var 2:
best............ 1.000000e+00
mean............ 4.177636e+02
variance........ 1.191460e+05
var 3:
best............ 1.000000e+00
mean............ 3.779018e+02
variance........ 8.873178e+04
var 4:
best............ 1.000000e+00
mean............ 2.473030e+02
variance........ 8.232235e+04

GENERATION: 2
Lexical Fit..... 1.085711e-02  5.588192e-02  2.121869e-01  2.122577e-01  8.836725e-01  9.153209e-01  1.000000e+00  1.000000e+00  
#unique......... 64, #Total UniqueCount: 232
var 1:
best............ 1.000000e+00
mean............ 3.759119e+01
variance........ 1.569265e+04
var 2:
best............ 1.000000e+00
mean............ 3.452268e+02
variance........ 1.467445e+05
var 3:
best............ 1.000000e+00
mean............ 2.546990e+02
variance........ 7.908208e+04
var 4:
best............ 1.000000e+00
mean............ 1.209958e+02
variance........ 2.949719e+04

GENERATION: 3
Lexical Fit..... 1.085711e-02  5.588192e-02  2.121869e-01  2.122577e-01  8.836725e-01  9.153209e-01  1.000000e+00  1.000000e+00  
#unique......... 59, #Total UniqueCount: 291
var 1:
best............ 1.000000e+00
mean............ 3.085583e+01
variance........ 1.043729e+04
var 2:
best............ 1.000000e+00
mean............ 4.340127e+02
variance........ 1.568525e+05
var 3:
best............ 1.000000e+00
mean............ 3.168519e+02
variance........ 6.753843e+04
var 4:
best............ 1.000000e+00
mean............ 1.304737e+02
variance........ 3.195516e+04

GENERATION: 4
Lexical Fit..... 1.085711e-02  5.588192e-02  2.121869e-01  2.122577e-01  8.836725e-01  9.153209e-01  1.000000e+00  1.000000e+00  
#unique......... 58, #Total UniqueCount: 349
var 1:
best............ 1.000000e+00
mean............ 2.325519e+01
variance........ 7.583676e+03
var 2:
best............ 1.000000e+00
mean............ 3.693504e+02
variance........ 1.531485e+05
var 3:
best............ 1.000000e+00
mean............ 2.826824e+02
variance........ 6.944398e+04
var 4:
best............ 1.000000e+00
mean............ 1.084883e+02
variance........ 1.926060e+04

GENERATION: 5
Lexical Fit..... 1.085711e-02  5.588192e-02  2.121869e-01  2.122577e-01  8.836725e-01  9.153209e-01  1.000000e+00  1.000000e+00  
#unique......... 60, #Total UniqueCount: 409
var 1:
best............ 1.000000e+00
mean............ 2.262238e+01
variance........ 5.021294e+03
var 2:
best............ 1.000000e+00
mean............ 4.082041e+02
variance........ 1.744149e+05
var 3:
best............ 1.000000e+00
mean............ 2.850748e+02
variance........ 7.121599e+04
var 4:
best............ 1.000000e+00
mean............ 1.063110e+02
variance........ 2.060405e+04

GENERATION: 6
Lexical Fit..... 1.085711e-02  5.588192e-02  2.121869e-01  2.122577e-01  8.836725e-01  9.153209e-01  1.000000e+00  1.000000e+00  
#unique......... 57, #Total UniqueCount: 466
var 1:
best............ 1.000000e+00
mean............ 1.822618e+01
variance........ 4.503182e+03
var 2:
best............ 1.000000e+00
mean............ 3.757066e+02
variance........ 1.523975e+05
var 3:
best............ 1.000000e+00
mean............ 2.999702e+02
variance........ 8.646708e+04
var 4:
best............ 1.000000e+00
mean............ 8.528497e+01
variance........ 1.511637e+04

'wait.generations' limit reached.
No significant improvement in 5 generations.

Solution Lexical Fitness Value:
1.085711e-02  5.588192e-02  2.121869e-01  2.122577e-01  8.836725e-01  9.153209e-01  1.000000e+00  1.000000e+00  

Parameters at the Solution:

 X[ 1] :    1.000000e+00
 X[ 2] :    1.000000e+00
 X[ 3] :    1.000000e+00
 X[ 4] :    1.000000e+00

Solution Found Generation 1
Number of Generations Run 6

Sun Nov 26 14:43:22 2023
Total run time : 0 hours 1 minutes and 9 seconds

mgen3 <- Match(Tr=Tr, X=X, Weight.matrix=gen3)
MatchBalance(Tr~size + stories + age + class, data=gb, match.out=mgen3, nboots=1000)

***** (V1) size *****
                       Before Matching       After Matching
mean treatment........     326101            326101 
mean control..........     226158            323438 
std mean diff.........     34.366           0.91569 

mean raw eQQ diff.....     106293              9063 
med  raw eQQ diff.....     111749              4337 
max  raw eQQ diff.....    2059803            148788 

mean eCDF diff........    0.16972          0.006727 
med  eCDF diff........    0.20193         0.0052562 
max  eCDF diff........    0.27229          0.036137 

var ratio (Tr/Co).....    0.95638            1.0233 
T-test p-value........ < 2.22e-16          0.013972 
KS Bootstrap p-value.. < 2.22e-16             0.246 
KS Naive p-value...... < 2.22e-16            0.2734 
KS Statistic..........    0.27229          0.036137 


***** (V2) stories *****
                       Before Matching       After Matching
mean treatment........     15.343            15.343 
mean control..........     13.424            15.299 
std mean diff.........     14.413           0.33174 

mean raw eQQ diff.....      1.947           0.48555 
med  raw eQQ diff.....          2                 0 
max  raw eQQ diff.....         34                14 

mean eCDF diff........   0.027321         0.0067017 
med  eCDF diff........    0.01588         0.0052562 
max  eCDF diff........    0.08163          0.025624 

var ratio (Tr/Co).....      1.191            1.0517 
T-test p-value........ 0.00032045           0.45696 
KS Bootstrap p-value.. < 2.22e-16             0.567 
KS Naive p-value...... 0.00051562           0.69976 
KS Statistic..........    0.08163          0.025624 


***** (V3) age *****
                       Before Matching       After Matching
mean treatment........     23.898            23.898 
mean control..........     49.308            24.074 
std mean diff.........    -162.69           -1.1274 

mean raw eQQ diff.....     25.454           0.70565 
med  raw eQQ diff.....         14                 0 
max  raw eQQ diff.....         63                 8 

mean eCDF diff........    0.17859         0.0076627 
med  eCDF diff........    0.15303         0.0052562 
max  eCDF diff........    0.44503          0.036137 

var ratio (Tr/Co).....    0.23341            1.0146 
T-test p-value........ < 2.22e-16          0.083604 
KS Bootstrap p-value.. < 2.22e-16             0.186 
KS Naive p-value...... < 2.22e-16            0.2734 
KS Statistic..........    0.44503          0.036137 


***** (V4) class *****
                       Before Matching       After Matching
mean treatment........      1.215             1.215 
mean control..........     1.7929             1.215 
std mean diff.........    -132.68                 0 

mean raw eQQ diff.....    0.57879                 0 
med  raw eQQ diff.....          1                 0 
max  raw eQQ diff.....          1                 0 

mean eCDF diff........    0.19262                 0 
med  eCDF diff........    0.14373                 0 
max  eCDF diff........    0.43413                 0 

var ratio (Tr/Co).....    0.40157                 1 
T-test p-value........ < 2.22e-16                 1 
KS Bootstrap p-value.. < 2.22e-16                 1 
KS Naive p-value...... < 2.22e-16                 1 
KS Statistic..........    0.43413                 0 


Before Matching Minimum p.value: < 2.22e-16 
Variable Name(s): size stories age class  Number(s): 1 2 3 4 

After Matching Minimum p.value: 0.013972 
Variable Name(s): size  Number(s): 1 

mgenout_caliper <- Match(Y=Y, Tr=Tr, X=X, Weight.matrix=gen3)
summary(mgenout_caliper)

Estimate...  2.6013 
AI SE......  0.86088 
T-stat.....  3.0216 
p.val......  0.0025141 

Original number of observations..............  7820 
Original number of treated obs...............  679 
Matched number of observations...............  679 
Matched number of observations  (unweighted).  1522 

# Quantile effect with Matched Data

mdt <- gb[mgen1$index.treated, ] 
mdc <- gb[mgen1$index.control, ] 

MQ10TE <- quantile(mdt$leasing_rate, probs = 0.1) - quantile(mdc$leasing_rate, probs = 0.1)
cat("10% Quantile Treatment Effect with Matching:", MQ10TE)

10% Quantile Treatment Effect with Matching: 8.15

quantile(gb$leasing_rate,probs=0.45)

  45% 
87.91 

# Plotting Quantile Treatment Effects

library(ggplot2)

quantile_levels <- seq(0.01, 0.99, by = 0.01)
quantile_treatment_effects <- sapply(quantile_levels, function(q) {
  quantile(mdt$leasing_rate, probs = q) - quantile(mdc$leasing_rate, probs = q)
})

plot_data <- data.frame(Quantile = quantile_levels, TreatmentEffect = quantile_treatment_effects)

ggplot(plot_data, aes(x = Quantile, y = TreatmentEffect)) +
  geom_point() +
  theme_minimal() +
  labs(title = "Quantile Treatment Effect of Green Rating on Leasing Rate",
       x = "Quantile",
       y = "Treatment Effect") +
  theme(plot.title = element_text(hjust = 0.5))

# Sensitivity Analysis using "class" as a benchmark covariate

library(quantreg)
library(sensemakr)

matched_data <- rbind(mdt, mdc)

# Linear model, removing post-treatment and irrelevant covariates.
lm <- lm(leasing_rate ~ . -CS_PropertyID - rev_psf - Rent - class_a - class_b, data = matched_data)
summary(lm)

Call:
lm(formula = leasing_rate ~ . - CS_PropertyID - rev_psf - Rent - 
    class_a - class_b, data = matched_data)

Residuals:
    Min      1Q  Median      3Q     Max 
-84.357  -3.897   3.040   8.063  18.592 

Coefficients:
                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)       7.913e+01  1.386e+00  57.095  < 2e-16 ***
size              8.745e-07  1.955e-06   0.447 0.654707    
City_Market_Rent  2.098e-01  2.695e-02   7.784 9.54e-15 ***
stories           1.602e-01  4.357e-02   3.676 0.000241 ***
age               3.009e-02  1.665e-02   1.807 0.070903 .  
renovated         1.038e+00  6.586e-01   1.577 0.115005    
class            -1.408e+00  6.803e-01  -2.070 0.038499 *  
green_rating      2.292e+00  4.925e-01   4.654 3.40e-06 ***
LEED              8.338e-01  1.155e+00   0.722 0.470554    
amenities         1.188e-01  6.193e-01   0.192 0.847882    
Utility_Costs    -7.406e-01  2.951e-01  -2.510 0.012137 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 13.19 on 3061 degrees of freedom
Multiple R-squared:  0.06816,   Adjusted R-squared:  0.06512 
F-statistic: 22.39 on 10 and 3061 DF,  p-value: < 2.2e-16

# Sensitivity Analysis using "class" as the benchmark.
sensitivity <- sensemakr(model = lm, 
                  treatment = "green_rating",
                  benchmark_covariates = "class",
                  kd = c(1, seq(10, 140, by=1)), #change by=1 to get precise location where 9.11% is surpassed
                  q = 1,
                  alpha = 0.05, 
                  reduce = TRUE)

plot(sensitivity,label.text=FALSE)

summary(sensitivity)

Sensitivity Analysis to Unobserved Confounding

Model Formula: leasing_rate ~ (CS_PropertyID + rev_psf + Rent + size + City_Market_Rent + 
    stories + age + renovated + class + green_rating + LEED + 
    amenities + Utility_Costs + class_a + class_b) - CS_PropertyID - 
    rev_psf - Rent - class_a - class_b

Null hypothesis: q = 1 and reduce = TRUE 
-- This means we are considering biases that reduce the absolute value of the current estimate.
-- The null hypothesis deemed problematic is H0:tau = 0 

Unadjusted Estimates of 'green_rating': 
  Coef. estimate: 2.2919 
  Standard Error: 0.4925 
  t-value (H0:tau = 0): 4.6538 

Sensitivity Statistics:
  Partial R2 of treatment with outcome: 0.007 
  Robustness Value, q = 1: 0.0807 
  Robustness Value, q = 1, alpha = 0.05: 0.0475 

Verbal interpretation of sensitivity statistics:

-- Partial R2 of the treatment with the outcome: an extreme confounder (orthogonal to the covariates) that explains 100% of the residual variance of the outcome, would need to explain at least 0.7% of the residual variance of the treatment to fully account for the observed estimated effect.

-- Robustness Value, q = 1: unobserved confounders (orthogonal to the covariates) that explain more than 8.07% of the residual variance of both the treatment and the outcome are strong enough to bring the point estimate to 0 (a bias of 100% of the original estimate). Conversely, unobserved confounders that do not explain more than 8.07% of the residual variance of both the treatment and the outcome are not strong enough to bring the point estimate to 0.

-- Robustness Value, q = 1, alpha = 0.05: unobserved confounders (orthogonal to the covariates) that explain more than 4.75% of the residual variance of both the treatment and the outcome are strong enough to bring the estimate to a range where it is no longer 'statistically different' from 0 (a bias of 100% of the original estimate), at the significance level of alpha = 0.05. Conversely, unobserved confounders that do not explain more than 4.75% of the residual variance of both the treatment and the outcome are not strong enough to bring the estimate to a range where it is no longer 'statistically different' from 0, at the significance level of alpha = 0.05.

Bounds on omitted variable bias:

--The table below shows the maximum strength of unobserved confounders with association with the treatment and the outcome bounded by a multiple of the observed explanatory power of the chosen benchmark covariate(s).

ovb_minimal_reporting(sensitivity, format = "latex",verbose=TRUE)

\begin{table}[!h]
\centering
\begin{tabular}{lrrrrrr}
\multicolumn{7}{c}{Outcome: \textit{leasing_rate}} \\
\hline \hline 
Treatment: & Est. & S.E. & t-value & $R^2_{Y \sim D |{\bf X}}$ & $RV_{q = 1}$ & $RV_{q = 1, \alpha = 0.05}$  \\ 
\hline 
\textit{green_rating} & 2.292 & 0.492 & 4.654 & 0.7\% & 8.1\% & 4.8\% \\ 
\hline 
df = 3061 & & \multicolumn{5}{r}{ \small \textit{Bound (1x class)}: $R^2_{Y\sim Z| {\bf X}, D}$ = 0.1\%, $R^2_{D\sim Z| {\bf X} }$ = 0\%} \\
\end{tabular}
\end{table}

# Question 3

# Creating a synthetic control for Cantabria using base-code

library(Synth)
data(basque)

# dataprep: prepare data for synth
dataprep.out <-
  dataprep(
  foo = basque
  ,predictors= c("school.illit",
                 "school.prim",
                 "school.med",
                 "school.high",
                 "school.post.high"
                 ,"invest"
                 )
   ,predictors.op = c("mean")
   ,dependent     = c("gdpcap")
   ,unit.variable = c("regionno")
   ,time.variable = c("year")
   ,special.predictors = list(
    list("gdpcap",1960:1969,c("mean")),                            
    list("sec.agriculture",seq(1961,1969,2),c("mean")),
    list("sec.energy",seq(1961,1969,2),c("mean")),
    list("sec.industry",seq(1961,1969,2),c("mean")),
    list("sec.construction",seq(1961,1969,2),c("mean")),
    list("sec.services.venta",seq(1961,1969,2),c("mean")),
    list("sec.services.nonventa",seq(1961,1969,2),c("mean")),
    list("popdens",1969,c("mean")))
    ,treatment.identifier  = 7 #Cantabria
    ,controls.identifier   = c(2:6, 8:16, 18) #Removing 1 and 17, Espana and Basque
    ,time.predictors.prior = c(1964:1969)
    ,time.optimize.ssr     = c(1960:1969)
    ,unit.names.variable   = c("regionname")
    ,time.plot            = c(1955:1997) 
    )

# 1. combine highest and second highest 
# schooling category and eliminate highest category
dataprep.out$X1["school.high",] <- 
 dataprep.out$X1["school.high",] + 
 dataprep.out$X1["school.post.high",]
dataprep.out$X1                 <- 
 as.matrix(dataprep.out$X1[
  -which(rownames(dataprep.out$X1)=="school.post.high"),])
dataprep.out$X0["school.high",] <- 
 dataprep.out$X0["school.high",] + 
 dataprep.out$X0["school.post.high",]
dataprep.out$X0                 <- 
dataprep.out$X0[
 -which(rownames(dataprep.out$X0)=="school.post.high"),]

# 2. make total and compute shares for the schooling catgeories
lowest  <- which(rownames(dataprep.out$X0)=="school.illit")
highest <- which(rownames(dataprep.out$X0)=="school.high")

dataprep.out$X1[lowest:highest,] <- 
 (100 * dataprep.out$X1[lowest:highest,]) /
 sum(dataprep.out$X1[lowest:highest,])
dataprep.out$X0[lowest:highest,] <-  
 100 * scale(dataprep.out$X0[lowest:highest,],
             center=FALSE,
             scale=colSums(dataprep.out$X0[lowest:highest,])
                                                 )
    
# run synth
synth.out <- synth(data.prep.obj = dataprep.out)

X1, X0, Z1, Z0 all come directly from dataprep object.


**************** 
 searching for synthetic control unit  
 

**************** 
**************** 
**************** 

MSPE (LOSS V): 7.829298e-05 

solution.v:
 0.08472248 0.07074392 0.03613354 0.004143408 0.2590285 0.2649847 0.09142931 0.001807713 0.04189152 0.01718393 0.05446338 0.02163412 0.05183345 

solution.w:
 6.5348e-06 1.10812e-05 0.4175669 0.001261402 0.06308619 1.3719e-06 2.5961e-06 0.09360902 0.4244228 3.8971e-06 2.1343e-06 1.10545e-05 8.6368e-06 4.2692e-06 2.1614e-06 

# Get result tables
synth.tables <- synth.tab(
                          dataprep.res = dataprep.out,
                          synth.res = synth.out
                          ) 

# results tables:
print(synth.tables)

$tab.pred
                                        Treated Synthetic Sample Mean
school.illit                              2.819     8.959      11.527
school.prim                              86.890    82.856      80.513
school.med                                7.233     5.589       5.307
school.high                               3.058     2.596       2.654
invest                                   29.071    23.345      20.914
special.gdpcap.1960.1969                  3.871     3.871       3.562
special.sec.agriculture.1961.1969        15.922    14.974      21.715
special.sec.energy.1961.1969              2.894     9.698       5.472
special.sec.industry.1961.1969           36.530    26.371      21.484
special.sec.construction.1961.1969        5.976     7.565       7.362
special.sec.services.venta.1961.1969     33.484    35.751      36.731
special.sec.services.nonventa.1961.1969   5.198     5.646       7.239
special.popdens.1969                     87.390   119.678     100.215

$tab.v
                                        v.weights
school.illit                            0.085    
school.prim                             0.071    
school.med                              0.036    
school.high                             0.004    
invest                                  0.259    
special.gdpcap.1960.1969                0.265    
special.sec.agriculture.1961.1969       0.091    
special.sec.energy.1961.1969            0.002    
special.sec.industry.1961.1969          0.042    
special.sec.construction.1961.1969      0.017    
special.sec.services.venta.1961.1969    0.054    
special.sec.services.nonventa.1961.1969 0.022    
special.popdens.1969                    0.052    

$tab.w
   w.weights                   unit.names unit.numbers
2      0.000                    Andalucia            2
3      0.000                       Aragon            3
4      0.418       Principado De Asturias            4
5      0.001             Baleares (Islas)            5
6      0.063                     Canarias            6
8      0.000              Castilla Y Leon            8
9      0.000           Castilla-La Mancha            9
10     0.094                     Cataluna           10
11     0.424         Comunidad Valenciana           11
12     0.000                  Extremadura           12
13     0.000                      Galicia           13
14     0.000        Madrid (Comunidad De)           14
15     0.000           Murcia (Region de)           15
16     0.000 Navarra (Comunidad Foral De)           16
18     0.000                   Rioja (La)           18

$tab.loss
       Loss W       Loss V
[1,] 1.060832 7.829298e-05

# plot results:
# path
path.plot(synth.res = synth.out,
          dataprep.res = dataprep.out,
          Ylab = c("Real per-capita GDP (1986 USD, thousand)"),
          Xlab = c("Year"), 
          Ylim = c(0,13), 
          Legend = c("Cantabria Region","Synthetic Cantabria Region"),
          ) 

## gaps
gaps.plot(synth.res = synth.out,
          dataprep.res = dataprep.out, 
          Ylab = c("Gap in Real per-capita GDP (1986 USD, thousand)"),
          Xlab = c("Year"), 
          Ylim = c(-1.5,1.5), 
          )

NA
NA

# Re Running Synthetic Control with comparison

library(Synth)
data(basque)

# Full-time Optimized
dataprep.out <-
  dataprep(
  foo = basque
  ,predictors= c("school.illit",
                 "school.prim",
                 "school.med",
                 "school.high",
                 "school.post.high"
                 ,"invest"
                 )
   ,predictors.op = c("mean")
   ,dependent     = c("gdpcap")
   ,unit.variable = c("regionno")
   ,time.variable = c("year")
   ,special.predictors = list(
    list("gdpcap",1960:1969,c("mean")),                            
    list("sec.agriculture",seq(1961,1969,2),c("mean")),
    list("sec.energy",seq(1961,1969,2),c("mean")),
    list("sec.industry",seq(1961,1969,2),c("mean")),
    list("sec.construction",seq(1961,1969,2),c("mean")),
    list("sec.services.venta",seq(1961,1969,2),c("mean")),
    list("sec.services.nonventa",seq(1961,1969,2),c("mean")),
    list("popdens",1969,c("mean")))
    ,treatment.identifier  = 7 #Cantabria
    ,controls.identifier   = c(2:6, 8:16, 18) #Removing 1, 17
    ,time.predictors.prior = c(1955:1997) #Full-time optimization
    ,time.optimize.ssr     = c(1955:1997)
    ,unit.names.variable   = c("regionname")
    ,time.plot            = c(1955:1997) 
    )

 Missing data- treated unit; predictor: school.illit ; for period: 1955 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1956 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1957 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1958 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1959 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1960 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1961 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1962 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1963 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1970 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1971 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1972 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1973 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1974 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1975 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1976 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1977 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1978 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1979 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1980 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1981 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1982 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1983 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1984 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1985 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1986 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1987 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1988 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1989 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1990 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1991 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1992 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1993 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1994 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1995 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1996 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.illit ; for period: 1997 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1955 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1956 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1957 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1958 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1959 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1960 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1961 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1962 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1963 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1970 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1971 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1972 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1973 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1974 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1975 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1976 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1977 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1978 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1979 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1980 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1981 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1982 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1983 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1984 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1985 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1986 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1987 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1988 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1989 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1990 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1991 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1992 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1993 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1994 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1995 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1996 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.prim ; for period: 1997 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1955 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1956 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1957 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1958 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1959 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1960 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1961 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1962 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1963 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1970 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1971 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1972 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1973 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1974 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1975 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1976 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1977 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1978 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1979 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1980 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1981 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1982 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1983 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1984 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1985 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1986 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1987 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1988 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1989 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1990 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1991 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1992 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1993 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1994 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1995 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1996 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.med ; for period: 1997 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1955 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1956 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1957 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1958 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1959 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1960 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1961 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1962 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1963 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1970 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1971 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1972 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1973 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1974 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1975 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1976 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1977 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1978 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1979 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1980 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1981 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1982 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1983 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1984 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1985 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1986 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1987 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1988 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1989 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1990 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1991 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1992 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1993 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1994 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1995 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1996 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.high ; for period: 1997 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1955 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1956 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1957 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1958 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1959 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1960 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1961 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1962 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1963 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1970 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1971 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1972 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1973 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1974 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1975 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1976 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1977 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1978 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1979 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1980 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1981 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1982 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1983 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1984 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1985 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1986 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1987 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1988 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1989 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1990 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1991 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1992 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1993 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1994 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1995 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1996 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: school.post.high ; for period: 1997 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: invest ; for period: 1955 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: invest ; for period: 1956 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: invest ; for period: 1957 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: invest ; for period: 1958 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: invest ; for period: 1959 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: invest ; for period: 1960 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: invest ; for period: 1961 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: invest ; for period: 1962 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: invest ; for period: 1963 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: invest ; for period: 1996 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data- treated unit; predictor: invest ; for period: 1997 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.illit ; for period: 1955 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.illit ; for period: 1956 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.illit ; for period: 1957 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.illit ; for period: 1958 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.illit ; for period: 1959 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.illit ; for period: 1960 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.prim ; for period: 1955 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.prim ; for period: 1956 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.prim ; for period: 1957 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.prim ; for period: 1958 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.prim ; for period: 1959 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.prim ; for period: 1960 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.med ; for period: 1955 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.med ; for period: 1956 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.med ; for period: 1957 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.med ; for period: 1958 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.med ; for period: 1959 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.med ; for period: 1960 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.high ; for period: 1955 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.high ; for period: 1956 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.high ; for period: 1957 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.high ; for period: 1958 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.high ; for period: 1959 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.high ; for period: 1960 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.post.high ; for period: 1955 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.post.high ; for period: 1956 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.post.high ; for period: 1957 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.post.high ; for period: 1958 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.post.high ; for period: 1959 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: school.post.high ; for period: 1960 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: invest ; for period: 1955 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: invest ; for period: 1956 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: invest ; for period: 1957 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: invest ; for period: 1958 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: invest ; for period: 1959 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

 Missing data - control unit: 2 ; predictor: invest ; for period: 1960 
 We ignore (na.rm = TRUE) all missing values for predictors.op.

# 1. combine highest and second highest 
# schooling category and eliminate highest category
dataprep.out$X1["school.high",] <- 
 dataprep.out$X1["school.high",] + 
 dataprep.out$X1["school.post.high",]
dataprep.out$X1                 <- 
 as.matrix(dataprep.out$X1[
  -which(rownames(dataprep.out$X1)=="school.post.high"),])
dataprep.out$X0["school.high",] <- 
 dataprep.out$X0["school.high",] + 
 dataprep.out$X0["school.post.high",]
dataprep.out$X0                 <- 
dataprep.out$X0[
 -which(rownames(dataprep.out$X0)=="school.post.high"),]

# 2. make total and compute shares for the schooling catgeories
lowest  <- which(rownames(dataprep.out$X0)=="school.illit")
highest <- which(rownames(dataprep.out$X0)=="school.high")

dataprep.out$X1[lowest:highest,] <- 
 (100 * dataprep.out$X1[lowest:highest,]) /
 sum(dataprep.out$X1[lowest:highest,])
dataprep.out$X0[lowest:highest,] <-  
 100 * scale(dataprep.out$X0[lowest:highest,],
             center=FALSE,
             scale=colSums(dataprep.out$X0[lowest:highest,])
                                                 )
# run synth
synth.out <- synth(data.prep.obj = dataprep.out)

X1, X0, Z1, Z0 all come directly from dataprep object.


**************** 
 searching for synthetic control unit  
 

**************** 
**************** 
**************** 

MSPE (LOSS V): 0.06148385 

solution.v:
 0.001583569 0.009615875 0.001709211 0.009467179 0.438055 0.1711221 0.1236533 0.01725706 0.0238148 0.06942482 0.02239812 0.08142432 0.03047454 

solution.w:
 6.727e-07 5.2411e-06 7.5286e-06 5.831e-07 6.315e-07 6.1372e-06 0.1080418 2.866e-07 0.8919265 3.9899e-06 5.308e-07 3.229e-07 1.1019e-06 3.6378e-06 1.0246e-06 

# Get result tables
synth.tables <- synth.tab(
                          dataprep.res = dataprep.out,
                          synth.res = synth.out
                          ) 

Cantabria_Synthetic_Path_1 <- dataprep.out$Y0plot %*% synth.out$solution.w

# Basque-period Optimized
dataprep.out <-
  dataprep(
  foo = basque
  ,predictors= c("school.illit",
                 "school.prim",
                 "school.med",
                 "school.high",
                 "school.post.high"
                 ,"invest"
                 )
   ,predictors.op = c("mean")
   ,dependent     = c("gdpcap")
   ,unit.variable = c("regionno")
   ,time.variable = c("year")
   ,special.predictors = list(
    list("gdpcap",1960:1969,c("mean")),                            
    list("sec.agriculture",seq(1961,1969,2),c("mean")),
    list("sec.energy",seq(1961,1969,2),c("mean")),
    list("sec.industry",seq(1961,1969,2),c("mean")),
    list("sec.construction",seq(1961,1969,2),c("mean")),
    list("sec.services.venta",seq(1961,1969,2),c("mean")),
    list("sec.services.nonventa",seq(1961,1969,2),c("mean")),
    list("popdens",1969,c("mean")))
    ,treatment.identifier  = 7 #Cantabria
    ,controls.identifier   = c(2:6, 8:16, 18) #Removing 1, 17
    ,time.predictors.prior = c(1964:1969) #Basque-time optimization
    ,time.optimize.ssr     = c(1960:1969)
    ,unit.names.variable   = c("regionname")
    ,time.plot            = c(1955:1997) 
    )

# 1. combine highest and second highest 
# schooling category and eliminate highest category
dataprep.out$X1["school.high",] <- 
 dataprep.out$X1["school.high",] + 
 dataprep.out$X1["school.post.high",]
dataprep.out$X1                 <- 
 as.matrix(dataprep.out$X1[
  -which(rownames(dataprep.out$X1)=="school.post.high"),])
dataprep.out$X0["school.high",] <- 
 dataprep.out$X0["school.high",] + 
 dataprep.out$X0["school.post.high",]
dataprep.out$X0                 <- 
dataprep.out$X0[
 -which(rownames(dataprep.out$X0)=="school.post.high"),]

# 2. make total and compute shares for the schooling catgeories
lowest  <- which(rownames(dataprep.out$X0)=="school.illit")
highest <- which(rownames(dataprep.out$X0)=="school.high")

dataprep.out$X1[lowest:highest,] <- 
 (100 * dataprep.out$X1[lowest:highest,]) /
 sum(dataprep.out$X1[lowest:highest,])
dataprep.out$X0[lowest:highest,] <-  
 100 * scale(dataprep.out$X0[lowest:highest,],
             center=FALSE,
             scale=colSums(dataprep.out$X0[lowest:highest,])
                                                 )
# run synth
synth.out <- synth(data.prep.obj = dataprep.out)

X1, X0, Z1, Z0 all come directly from dataprep object.


**************** 
 searching for synthetic control unit  
 

**************** 
**************** 
**************** 

MSPE (LOSS V): 7.829298e-05 

solution.v:
 0.08472248 0.07074392 0.03613354 0.004143408 0.2590285 0.2649847 0.09142931 0.001807713 0.04189152 0.01718393 0.05446338 0.02163412 0.05183345 

solution.w:
 6.5348e-06 1.10812e-05 0.4175669 0.001261402 0.06308619 1.3719e-06 2.5961e-06 0.09360902 0.4244228 3.8971e-06 2.1343e-06 1.10545e-05 8.6368e-06 4.2692e-06 2.1614e-06 

# Get result tables
synth.tables <- synth.tab(
                          dataprep.res = dataprep.out,
                          synth.res = synth.out
                          ) 

Cantabria_Synthetic_Path_2 <- dataprep.out$Y0plot %*% synth.out$solution.w

Cantabria_Real_Path <- basque[basque$regionname=='Cantabria',]$gdpcap

# Plotting
synthetic_df <- data.frame(X = rep(c(1955:1997),3),Y=c(rbind(Cantabria_Synthetic_Path_1,Cantabria_Synthetic_Path_2),Cantabria_Real_Path), method=c(rep("Full-period Optimized", 43),rep('Basque-period Optimized',43),rep('Cantabria Region', 43)))
library(ggplot2)
ggplot(data=synthetic_df, aes(x=X, y=Y, group=method)) +
  geom_line(aes(color=method))+
  theme(aspect.ratio=1/3)+
  xlab('Year')+
  ylab('Real per-capita GDP (1986 USD, thousand)')

synthetic_df

#Gap plot
gap_df <- data.frame(X = rep(c(1955:1997),2),
                     Y = rbind(Cantabria_Synthetic_Path_1 - Cantabria_Real_Path,
                             Cantabria_Synthetic_Path_2 - Cantabria_Real_Path),
                     method=c(rep("Full-period Optimized", 43),rep('Basque-period Optimized',43)))
#gap_df['Full-period Optimized'] <- Cantabria_Synthetic_Path_1 - Cantabria_Real_Path
#gap_df['Basque-period Optimized'] <- Cantabria_Synthetic_Path_2 - Cantabria_Real_Path

ggplot(data=gap_df, aes(x=X, y=w.weight, group=method)) +
  geom_line(aes(color=method))+
  theme(aspect.ratio=1/3)+
  xlab('Year')+
  ylab('Gaps in Real per-capita GDP (1986 USD, thousand)')+
  geom_hline(yintercept=0)+
  ylim(-1.5,1.5)

colnames(gap_df)

[1] "X"        "w.weight" "method"